Chapter 14 — Answers (Part II)

Free PDF of official NCERT Class 12 Maths Part II answers covering all textbook exercises for Chapters 7–13 (Integrals through Probability). No sign-up or payment required to download.

This answer key provides final answers to every exercise in the NCERT Class 12 Mathematics Part II textbook. Coverage spans Chapter 7 (Integrals, Exercises 7.1–7.10 plus Miscellaneous), Chapter 8 (Application of Integrals, Exercise 8.1 plus Miscellaneous), Chapter 9 (Differential Equations, Exercises 9.1–9.5 plus Miscellaneous), Chapter 10 (Vector Algebra, Exercises 10.1–10.4 plus Miscellaneous), Chapter 11 (Three Dimensional Geometry, Exercises 11.1–11.2 plus Miscellaneous), Chapter 12 (Linear Programming, Exercise 12.1), and Chapter 13 (Probability, Exercises 13.1–13.3 plus Miscellaneous).

1. 01Chapter 7 — Integrals: answers for Exercises 7.1 through 7.10 and the Miscellaneous Exercise, covering standard integrals, substitution, partial fractions, integration by parts, and definite integrals.
2. 02Chapter 8 — Application of Integrals: answers for Exercise 8.1 and the Miscellaneous Exercise on area under curves.
3. 03Chapter 9 — Differential Equations: answers for Exercises 9.1–9.5 and the Miscellaneous Exercise, covering order/degree identification, variable-separable, homogeneous, and linear differential equations.
4. 04Chapter 10 — Vector Algebra: answers for Exercises 10.1–10.4 and the Miscellaneous Exercise on scalars, vectors, dot products, and cross products.
5. 05Chapter 11 — Three Dimensional Geometry: answers for Exercises 11.1–11.2 and the Miscellaneous Exercise on direction cosines, lines, and angles in 3D space.
6. 06Chapter 12 — Linear Programming: answers for Exercise 12.1 covering graphical method problems with maximum and minimum values of the objective function.
7. 07Chapter 13 — Probability: answers for Exercises 13.1–13.3 and the Miscellaneous Exercise on conditional probability, independence, Bayes' theorem, and Bernoulli trials.